as Floats for Paddle-wheels. 359 



from the axis of the wheel. It may be noticed that if the velo- 

 city of the vessel be equal to the velocity of rotation of the edges 

 of the blade nearest to the axis, then 



— =\cot7. 

 cor 



In practice it is found that the efficiency of a screw is greatest 

 when its pitch is about 25° ; with this pitch the limit of 6 must 

 be increased, otherwise the breadth of the wheel will be dimi- 

 nished; also it appears from the above cases, and from the 

 experiments already made, that the distance from the axis of the 

 screw-surface to the axis of the wheel should not be less than half 

 the radius of the wheel. 



If then we take a=1 and y=26^°, so that cot 7 = 2, then 



q=2( \/3 + cos c2 0-cos<9). 



If the limit for 6 be 25°, then the breadth of the wheel will be 

 y|-ths of the breadth in the case which has been already inves- 

 tigated. 



With these values of X aud 7 we get 



R = i /3i ft) 2 r 4 j L cos dd6- f tan" 1 q . cos Odd 



+ ^-^)^e\o S (i +q ^dd 



+ ( 2 ~ ^T 1 COs3 6 ' tan_1 9 ' dd \' 

 M = ift©V-T I ^^-f^cos^^-t^tan-^.cos^^ 



-jVoga+^vfl 



2 (2- — \ [ fg cos 6d0- ftan- 1 q . cos Odd ] 

 2^2- ^yicos 3 ^.tan- 1 g^"y. 



+ : 



